1. Field of the Invention
The present invention relates to a method for determining the effects of stress on a non-linear orthotropic missile structure. The method uses three dimensional non-axisymmetric stresses and resultant strains, margins of safety, displacements, rotations, and internal loads, and bending moments. The method takes into account unequal tension and compression properties of materials, as well as non-linear properties of material and non-linear geometric displacements.
2. Description of Prior Art
Previous methods use mathematical models for calculating behavior of missile surfaces under stress. Those mathematical models do not include three dimensional non-linear orthotropic terms. An orthotropic missile structure is a missile structure that has special elastic properties. These elastic properties have considerable variation in two or more directions that are perpendicular to one another.
Thus a structural analysis method of the prior art, when using such a prior art mathematical model, would not accurately provide the true behavior of a missile structure to stress in three dimensions.
A method of more accurately predicting the three dimensional behavior of a missile structure to stresses is disclosed. The method uses a mathematical model of the missile structure. The mathematical model contains three dimensional non-linear orthotropic terms. With the new method an improved representation of the behavior of a missile structure may be obtained. In addition, the effects of changing temperature can be included in the method.
The present method has been developed for the structural analysis of rocket motor chambers, and similar structures such as rocket nozzles. During service use, these structures are subjected to non-axisymmetric, very general, and complex loading conditions. Such structures are constructed of nonlinear orthotropic materials. The model was developed with extended capabilities, not general available in existing computer codes. Specifically, the present method is capable of solving problems with any or all of the following characteristics:
1. Structures that are not axisymmetric, such as motor chambers with local non-axisymmetric imperfections (manufacturing anomalies or service damage). The mathematical model does not require idealization of a problem into a 2D problem. PA1 2. The structure may be manufactured from orthotropic non-linear materials. The present method has special orthotropic non-linear capabilities. It is not limited to orthotropic linear structures. PA1 3. The material may have different properties in tension and compression. The present method accounts for different tension/compression material properties. PA1 4. The present method is designed to handle large problems efficiently. There is no limitation on a number of elements or nodes. The method is easily portable to take full advantage of resources of large computers. PA1 5. Structure may be subjected to arbitrary loads. PA1 6. Buckling loads may be predicted with the program. PA1 1. The rocket chamber is constructed of multiple plies of filament winding. The fibers in the layers are in different directions. The fibers are the load resisting members. There are circumferential plies to resist hoop loads. There are polar plies to resist axial loads. A continuum code is required to predict accurately interlaminar shear stresses and normal stresses between the layers and stress concentrations due to non-axisymmetric flaws. PA1 2. The chamber material is orthotropic because the fiber modulus is extremely high relative to the resin modulus. The mechanical properties can be sizably different in the three principal material directions. The shear and compression properties of typical chamber material are sizably non-linear. This necessitates use of a method that can handle non-linear orthotropic material properties. PA1 3. The motor material properties are sizable different in tension from compression. Test data indicates certain nozzle materials may exhibit at elevated temperature tension properties which are different from compression by a factor of 20. This necessitates a code which accurately accounts for this difference in tension/compression properties. PA1 4. The chamber can have manufacturing anomalies and/or service damage which are not axisymmetric. This necessitates a code capable of handling 3D geometries. PA1 5. The chamber and nozzle are typically subjected to non-axisymmetric loads, including concentrated loads due to surge, mechanical fasteners and attachments, actuators, etc. PA1 6. The chamber must be designed to resist buckling, and to maintain positive margins of safety with respect to strength. PA1 7. The chamber is a pressure vessel and must be designed to sustain internal pressure loads.
The method can analyze a rocket motor that has the following unique characteristics. Such characteristics complicate the structural analysis:
In order to address the problem described above, it is necessary to utilize a theory which incorporates an incremental formulation to model complex path-dependent, non-linear material behavior.
The structural problems at which the present method is aimed are highly nonlinear due to both geometric and material nonlinearities. To handle these nonlinearities, the equilibrium equations are formulated in an incremental format.
The 3D motor geometry is idealized with isoparametric continuum elements which are able interlaminar normal and shear stresses. The use of 3D elements permits modelling of flaws and non-axisymmetric geometries. The element is described in Section 3.
The material properties are permitted to be non-linear with different tension/compression mechanical properties. The properties are described by piecewise linear functions of strain. No assumptions are made with regard to the properties having identical ratios of modulus slope in all 3 directions and shear. These are permitted to be arbitrary, and are permitted to conform exactly to the test data. No restrictions are made with regard to the number of piece-wise linear segments used to described the tension, compression and shear properties as a function of strain.
The response of the structure to load is non-linear because of possible large deformations, and the non-linear behavior of the material. Consequently, the load must be applied in increments and the solution obtained by iteration at each load step. The incremental procedure allows one to predict accurately path-dependent material behavior and buckling loads which is not possible with deformation type codes.